
Thus, with \(t \ge 1/\epsilon ^4\) , we have that \([(\Vert y\Vert _2^2 - 1)^2] \le \epsilon ^4\) . By Lemma 28 of [1]}, we obtain that \([\max (\Vert y\Vert _2^4,1)] \le (1+\epsilon ^2)^2 \le 1+3\epsilon ^2\) . Now, by Holder's inequality,
\([\max (\Vert y\Vert _2,1)] \le [\max (\Vert y\Vert _2,1)^4]^{1/4} \le (1+3\epsilon ^2)^{1/4} \le 1 + (3/4)\epsilon ^2.\) 
